28,099 research outputs found
A finite field approach to solving the Bethe Salpeter equation
We present a method to compute optical spectra and exciton binding energies
of molecules and solids based on the solution of the Bethe-Salpeter equation
(BSE) and the calculation of the screened Coulomb interaction in finite field.
The method does not require the explicit evaluation of dielectric matrices nor
of virtual electronic states, and can be easily applied without resorting to
the random phase approximation. In addition it utilizes localized orbitals
obtained from Bloch states using bisection techniques, thus greatly reducing
the complexity of the calculation and enabling the efficient use of hybrid
functionals to obtain single particle wavefunctions. We report exciton binding
energies of several molecules and absorption spectra of condensed systems of
unprecedented size, including water and ice samples with hundreds of atoms
The Gamow-Teller Resonance in Finite Nuclei in the Relativistic Random Phase Approximation
Gamow-Teller(GT) resonances in finite nuclei are studied in a fully
consistent relativistic random phase approximation (RPA) framework. A
relativistic form of the Landau-Migdal contact interaction in the spin-isospin
channel is adopted. This choice ensures that the GT excitation energy in
nuclear matter is correctly reproduced in the non-relativistic limit. The GT
response functions of doubly magic nuclei Ca, Zr and Pb
are calculated using the parameter set NL3 and =0.6 . It is found that
effects related to Dirac sea states account for a reduction of 6-7 % in the GT
sum rule.Comment: 9 pages, 1 figur
Communication Lower Bounds for Statistical Estimation Problems via a Distributed Data Processing Inequality
We study the tradeoff between the statistical error and communication cost of
distributed statistical estimation problems in high dimensions. In the
distributed sparse Gaussian mean estimation problem, each of the machines
receives data points from a -dimensional Gaussian distribution with
unknown mean which is promised to be -sparse. The machines
communicate by message passing and aim to estimate the mean . We
provide a tight (up to logarithmic factors) tradeoff between the estimation
error and the number of bits communicated between the machines. This directly
leads to a lower bound for the distributed \textit{sparse linear regression}
problem: to achieve the statistical minimax error, the total communication is
at least , where is the number of observations that
each machine receives and is the ambient dimension. These lower results
improve upon [Sha14,SD'14] by allowing multi-round iterative communication
model. We also give the first optimal simultaneous protocol in the dense case
for mean estimation.
As our main technique, we prove a \textit{distributed data processing
inequality}, as a generalization of usual data processing inequalities, which
might be of independent interest and useful for other problems.Comment: To appear at STOC 2016. Fixed typos in theorem 4.5 and incorporated
reviewers' suggestion
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